$$6p\cdot\frac{2}{p} = 1$$

$$ \begin{aligned} 6p\cdot\frac{2}{p} &= 1&& \text{multiply ALL terms by } \color{blue}{ p }. \\[1 em]p6p\cdot\frac{2}{p} &= p\cdot1&& \text{cancel out the denominators} \\[1 em]12p &= p&& \text{move the $ \color{blue}{ p } $ to the left side} \\[1 em]12p-p &= 0&& \text{simplify left side} \\[1 em]11p &= 0&& \text{ divide both sides by $ 11 $ } \\[1 em]p &= \frac{0}{11}&& \\[1 em]p &= 0&& \\[1 em] \end{aligned} $$

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